Everyone has a sense about what the term correlation means. It means
that the measurements of two properties are co-related. Let's explore
this a little more closely.

Intensity Measurement

Suppose that we measure fluorescence signals
at three wavelengths and call them I1, I2, and I3. Suppose that we get the following
set of measurements of these three intensities.

I1 (Counts per Second)

I2 (Counts per Second)

I3 (Counts per Second)

9012

2794

9412

21228

4011

8064

29903

5377

8554

41948

5815

8092

45223

7307

8194

61131

7893

9647

68245

9475

9390

78116

9852

8634

83310

11837

9900

90254

13183

8069

Relationships Between Measurements

In Figure 1 we plot I2 and I3 versus I1. When we see this kind of data our intuition says
that, yes, I2 and I1 are correlated because from a given value of I2 we can predict an
approximate value of I1. I3 and I1 are not well correlated because the value of I3 is
not a good predictor of the value of I1.

Figure 1: Correlation Between Intensities

Degree of Correlation

Typically, to assess the degree of correlation between two measurements we would next perform a linear regression, as shown in Figure 2, and
calculate the regression coefficient.

High Correlation

The black line in Figure 2 shows the linear fit between I2 and I1. The coefficient of correlation, R,
of this fit is 0.98. Perfect correlation has an R value of 1.00 (See Correlation Mathematics, below, for
the equation used to calculate R). So our intuition
is confirmed the two intensities are indeed highly correlated.

Low Correlation

The red line shows the linear fit between I3 and I1. The low R value of 0.18 confirms that these two
intensities are not highly correlated.

Figure 2: The Correlation Between Two Intensities. The lines indicate the linear least squares fit or regression lines.